A precision spring balance consists of a light pan of mass suspended from a vertical…
PHYSICS · Subjective · CBSE · Physics · Mechanical Properties of Solids · Mechanical Properties of Solids
Problem
A precision spring balance consists of a light pan of mass 0.15kg suspended from a vertical spring of negligible unstretched length. The spring itself has a mass of 0.20kg distributed uniformly along its length. When the empty pan is in equilibrium at rest on the Earth’s surface, the total extension of the spring is measured to be 3.0cm.
(i) Derive an expression for the effective force that the spring must supply when a body of mass m is placed on the pan, taking into account the weights of both the spring and the pan.
(ii) Hence obtain a formula that relates the additional extension Δx produced by placing the mass m on the pan to the value of m.
(iii) Using your result, determine the mass which must be placed in the pan to produce an additional extension of 2.5cm, given that the stiffness constant of the spring is 600N m−1.
(iv) Comment briefly on how ignoring the masses of the spring and pan would affect the mass value obtained in part (iii).